Problem: Let N be a positive even number.

We have a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N). Snuke is constructing another permutation of (1, 2, ..., N), q, following the procedure below.

First, let q be an empty sequence. Then, perform the following operation until p becomes empty:

* Select two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.



When p becomes empty, q will be a permutation of (1, 2, ..., N).

Find the lexicographically smallest permutation that can be obtained as q.

Constraints

* N is an even number.
* 2 ≤ N ≤ 2 × 10^5
* p is a permutation of (1, 2, ..., N).

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the lexicographically smallest permutation, with spaces in between.

Examples

Input

4
3 2 4 1


Output

3 1 2 4


Input

2
1 2


Output

1 2


Input

8
4 6 3 2 8 5 7 1


Output

3 1 2 7 4 6 8 5

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    int mod = 1_000_000_007;
    int inf = Integer.MAX_VALUE;

    void solve(){
        int n = ni();
        int[] p = new int[n];
        for(int i = 0; i < n; i++){
            p[i] = ni();
        }
        SegmentTree even = new SegmentTree(n);
        SegmentTree odd = new SegmentTree(n);
        for(int i = 0; i < n; i++){
            if(i%2==0) even.update(i, p[i], i);
            if(i%2==1) odd.update(i, p[i], i);
        }
        PriorityQueue<Pair> pq = new PriorityQueue<>(1, (a,b) -> Integer.compare(a.q[0],b.q[0]));
        int left = 0;
        int right = n;
        int[] q = even.query(left,right);
        pq.add(new Pair(left, right, q));
        ArrayList<Integer> ans = new ArrayList<>();
        while(!pq.isEmpty()){
            Pair tmp = pq.poll();
            if(tmp.l%2==0){
                ans.add(tmp.q[0]);
                q = odd.query(tmp.q[1]+1, tmp.r);
                ans.add(q[0]);
                if(tmp.l<tmp.q[1]) pq.add(new Pair(tmp.l, tmp.q[1], even.query(tmp.l, tmp.q[1])));
                if(tmp.q[1]+1 < q[1]) pq.add(new Pair(tmp.q[1]+1, q[1], odd.query(tmp.q[1]+1, q[1])));
                if(q[1]+1<tmp.r) pq.add(new Pair(q[1]+1, tmp.r, even.query(q[1]+1, tmp.r)));
            }
            if(tmp.l%2==1){
                ans.add(tmp.q[0]);
                q = even.query(tmp.q[1]+1, tmp.r);
                ans.add(q[0]);
                if(tmp.l<tmp.q[1]) pq.add(new Pair(tmp.l, tmp.q[1], odd.query(tmp.l, tmp.q[1])));
                if(tmp.q[1]+1 < q[1]) pq.add(new Pair(tmp.q[1]+1, q[1], even.query(tmp.q[1]+1, q[1])));
                if(q[1]+1<tmp.r) pq.add(new Pair(q[1]+1, tmp.r, odd.query(q[1]+1, tmp.r)));
            }
        }
        for(int i : ans){
            out.print(i+" ");
        }
        out.println();
    }


    class Pair{
        int l;
        int r;
        int[] q;
        Pair(int left, int right, int[] q){
            this.l = left;
            this.r = right;
            this.q = q;
        }
    }

    class SegmentTree {
        int n;
        int[][] seg;
        SegmentTree(int n) {
            this.n = Integer.highestOneBit(n) << 1;
            this.seg = new int[this.n<<1][2];
            for(int i=0;i<(this.n<<1);++i){
                seg[i][0] = inf;
                seg[i][1] = -1;
            }
        }
        int[] comb(int[] ans1, int[] ans2){
            if(ans1[0]<=ans2[0]){
                return new int[]{ans1[0], ans1[1]};
            }
            return new int[]{ans2[0], ans2[1]};
        }
        void update(int x, int value, int id) {
            x += n - 1;
            this.seg[x][0] = value;
            this.seg[x][1] = id;
            while (x > 0) {
                x = (x - 1) / 2;
                this.seg[x] = comb(this.seg[2 * x + 1], this.seg[2 * x + 2]);
            }
        }
        int[] query(int a,int b,int l,int r,int k){
            if(a<=l&&r<=b) return seg[k];
            if(b<=l||r<=a) return new int[]{inf, -1};
            int[] ans1=query(a,b,l,(l+r)/2,2*k+1);
            int[] ans2=query(a,b,(l+r)/2,r,2*k+2);
            return comb(ans1, ans2);
        }
        int[] query(int l, int r) {
            return query(l,r,0,n,0);
        }
    }

    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}